Question

12. Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into
a single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.
INCERT EXEMPLAR)​

Answer 1

Answer: Let the edges of three cubes be 3x, 4x and 5x respectively.

So, the volume of the cube after melting will be = (3x)³ + (4x)³ + (5x)³

= 9x³ + 64x³ + 125x³ = 216x³

Now, let a be the edge of the new cube so formed after melting

Then we have,

a3 = 216x3

a = 6x

We know that,

Diagonal of the cube = √(a2 + a2 + a2) = a√3

So, 12√3 = a√3

a = 12 cm

x = 12/6 = 2

Thus, the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.